What happens to the copper wire because of the moving magnet?

In this explainer, nosotros will learn how to describe the current induced in a wire that is placed in a irresolute magnetic field.

Consider a loop of conducting wire as shown below.

This wire carries no current because there is no potential difference betwixt any ii points in the wire causing charge to menstruation.

It is possible, however, to create a current in this loop—without using a cell or bombardment.

Imagine that we position a bar magnet near the wire as follows.

Some of the magnetic field lines from the magnet pass through the wire loop as shown beneath.

All the same, if the magnet and the wire remain stationary, there will exist no current in the wire.

However, if the magnet is set in movement, then the magnetic field experienced by the loop will change.

That is, when the loop lies in a different function of the magnet's field, the number of field lines passing through the loop—or the management of the field lines, or both—will be unlike. This is what we mean when we say the magnetic field through the wire is irresolute.

The changing magnetic field through the loop creates a current in the wire. This process is called electromagnetic induction.

Definition: Electromagnetic Consecration

When a loop of conducting wire is exposed to a changing magnetic field, a electric current volition be induced in the wire.

There are many ways for a wire to experience a irresolute magnetic field.

Consider once more our bar magnet and wire loop, this time with field lines omitted for clarity. We have seen that if they both are stationary, no electric current is induced, every bit shown below.

Withal, if the magnet is in motion (in whatsoever direction) while the wire remains withal, the magnetic field through the wire will alter over time and current will be induced in the wire as follows.

It is too possible for the magnet to be stationary while the wire moves equally shown below.

Once again, current is induced in the wire. Note that the wire could exist moving in any direction relative to the magnet and electric current would all the same exist induced.

Every bit long as the magnetic field source and the wire are moving relative to one another, current is induced in the wire.

Interestingly, the magnitude of electric current induced depends on how rapidly the field through the wire loop changes.

For example, imagine that the wire is stationary, while the magnet moves very slowly toward it, as depicted below.

The magnetic field through the wire will alter slowly, and the current induced in the wire volition be modest.

However, if the magnet instead moves very quickly toward the wire, a greater electric current volition exist induced as follows.

This greater induced electric current is caused past a greater charge per unit of change of the magnetic field through the wire.

There are withal other means of increasing induced current. These include increasing the strength of the magnet being used and calculation more loops to the wire.

Example one: Understanding Electromagnetic Consecration

The diagram shows a permanent magnet being moved through a loop of copper wire. This motion induces an electric current of 0.5 A in the wire.

1. If the magnet is moved through the loop at half the speed, what volition the current in the loop be?
2. If the permanent magnet is changed for one that is twice as strong and moves through the loop at the original speed, what will the current in the loop be?

Answer

Part 1

Moving at its initial speed, the bar magnet creates a change in the magnetic field through the copper loop such that a current of 0.5 A is induced.

The magnitude of induced current is direct related to the charge per unit at which the magnetic field through the loop changes, and therefore the magnet'due south speed.

A faster-moving magnet will therefore induce more current and a slower-moving magnet less current.

If the magnet moves at half its initial speed, the current in the loop will be less than 0.5 A.

Part 2

Considering a change in the magnet's strength, we recall that the current induced in the copper loop is due to the rate at which the magnetic field through the loop changes.

Increasing the magnet's strength means that the magnetic field through the loop will exist changing at a greater rate. A greater electric current will therefore be induced, so we can say that if the strength of the magnet is doubled and it moves at the same speed as earlier, and so more than 0.5 A of current will exist induced in the loop.

Some other way to strengthen induction is to replace a single loop of wire with a wire arranged in many identical loops, called a solenoid. Each loop or plough in a solenoid multiplies the induced potential difference in the wire. An case of a solenoid is shown below.

Example two: Understanding Relative Move in Electromagnetism

Role (a) of the diagram shows a bar magnet moving at a speed toward a stationary solenoid. This induces an electrical potential difference across the two ends of the solenoid. Part (b) of the diagram shows a stationary bar magnet, with a solenoid moving toward it at speed . How is the potential difference induced in the solenoid in part (b) different from that in part (a)?

Respond

Recall that a solenoid is a gyre of wire, as shown in the above diagrams.

In diagram (a), nosotros encounter the north pole of the bar magnet approaching the solenoid at a speed .

In diagram (b), the magnet is stationary while the solenoid at present approaches the magnet's north pole at the same speed .

The relative motility in both of these instances is the same; the magnet'due south north pole and the solenoid arroyo one another at speed .

Thus, the change in magnetic field through the solenoid'south loops is the aforementioned, whether the magnet is in motion or the solenoid.

This changing magnetic field is what induces a potential difference in the solenoid, so we expect the potential deviation induced to exist the same in both scenarios.

When a wire experiences a irresolute magnetic field, the direction of the induced current corresponds to the changing field.

Consider a bar magnet moving through a solenoid as shown below.

Current is induced in the solenoid, and this current creates its ain magnetic field.

As with whatever magnetic field, the induced field can exist modeled equally possessing a n and s pole. Effectively, the solenoid can be replaced with a bar magnet. The fields of these two objects are depicted below.

Supposing this exchange is made, the orientation of the magnet replacing the solenoid must be adamant. At that place are 2 possibilities for this orientation as shown below.

To make up one's mind which orientation is correct, nosotros consider the consequence of each 1 on the moving bar magnet.

In orientation A, the southward pole of the stationary magnet would concenter the moving magnet'south north pole. The moving magnet would then accelerate, manifesting a kinetic free energy that increases continually. This would imply that the total free energy of the isolated arrangement of magnets is increasing. The constabulary of conservation of free energy prohibits this from happening.

In orientation B, rather than attracting the moving magnet, the stationary magnet repels it. This slows down the moving magnet and somewhen stops information technology.

In light of energy conservation, the stationary magnet must have orientation B. It repels the incoming magnet and slows it down.

This result holds true regardless of the moving magnet'south orientation. Whichever of the magnet's poles is nearest to the wire it approaches, the wire can be considered as a bar magnet with opposing polarity.

Considering again a wire interacting with a irresolute magnetic field, we tin can now make a general statement almost the direction of current induced in the wire with respect to the direction of the changing external field.

Definition: Lenz's Law

When electric current is created through electromagnetic induction, the management of the current is such that it generates a magnetic field opposing the change in the original magnetic field.

Example three: Understanding Lenz's Law

The diagram shows a bar magnet moving abroad from a solenoid. This induces an electrical current in the solenoid, which creates its own magnetic field in turn. Which terminate of the solenoid is the north pole of the induced magnetic field?

Answer

Since the bar magnet is moving relative to the solenoid, the solenoid experiences a changing magnetic field.

Current is therefore induced in the solenoid, which in turn induces a magnetic field.

We are to consider this field every bit the field created by a magnet. The magnet's n pole is either at point A, with the south pole therefore at point B, or at point B, with the south pole at point A.

Allow'due south consider both of these options in turn.

If point A near the solenoid is a magnetic northward pole and signal B is a south pole, then the actual magnet and the magnet replacing the solenoid would appear every bit follows.

Since similar magnetic poles repel, we would expect the magnet on the left to exist pushed to the left. The magnet already moving that way would accelerate in that management.

The alternative to the above is for point A near the solenoid to be a south magnetic pole and for point B to be the due north magnetic pole. This is shown below.

Opposite magnetic poles attract, and so we would expect these two magnets to tend to draw closer together.

This arrangement of magnets would make the moving magnet slow downwards. Its motility to the left would exist opposed by an attraction to the south pole at point A.

Call up from Lenz's law that induced magnetic fields oppose the changing magnetic fields that crusade them. In this example, then, we are looking for the induced magnetic field that works against the motility of the magnet moving to the left.

An induced field that opposes this move will tend to pull the moving magnet to the correct. We take seen that a south magnetic pole at bespeak A has this effect.

Therefore, when the induced magnetic field of the solenoid has a due south magnetic pole at A, and a due north magnetic pole at B, the induced field and the irresolute external field interact as described by Lenz's law.

The northward magnetic pole of the induced field is at point B.

A potential difference can be induced across a wire even if the wire does non class a closed loop.

For example, a direct section of wire tin can move through a magnetic field—fifty-fifty a compatible i—in such a manner that a potential difference is established beyond the ends of the wire.

We can visualize this by picturing the wire as though it points into and out of the screen and the field equally pointing from right to left around the wire.

When the wire is at rest in this uniform field, no potential difference is induced. However, when the wire is put into motion so that it crosses magnetic field lines, a potential difference is induced across the wire.

The magnitude of the induced potential difference is proportional to the charge per unit at which the wire crosses magnetic field lines.

For a wire and field oriented as shown above, there are many directions in which the wire could move to cantankerous magnetic field lines and therefore induce a potential deviation.

Indeed, there are only 2 ways it could move so that a potential difference is not induced—parallel or antiparallel to the magnetic field.

A potential difference induced in a moving wire can be positive or negative. If the potential difference induced in a wire that moves vertically upward, for example, is positive, so the potential difference induced when the wire moves downward is negative.

Example 4: Understanding Electromagnetic Consecration

Parts (a), (b), (c), and (d) in the diagram show a direct slice of copper wire moving through a magnetic field. The magnetic field is uniform, and in each part the wire is moving at the aforementioned speed, but in a unlike direction through the magnetic field. Which of (a), (b), (c), and (d) shows the motion of the wire that would lead to the greatest potential difference being induced in information technology?

Answer

In each of the 4 diagrams, a copper wire with its axis pointing into and out of the screen moves through a uniform magnetic field.

Such motion is capable of inducing a potential divergence across the ends of the wire.

The magnitude of the potential difference induced is proportional to the rate at which the wire crosses magnetic field lines.

We are told that, in all iv cases, the speed of the moving wire is the aforementioned. Therefore, the merely gene affecting how quickly the wire crosses magnetic field lines is its direction of motion.

A wire moving to the left, for example, parallel to the magnetic field, will cantankerous no field lines and thus will not experience any induced electric current.

A wire moving perpendicularly to the field lines, nevertheless, will intersect those lines at the highest rate possible for its speed.

Diagrams (a), and (b) prove the wire moving at angles that are not with respect to the magnetic field. Diagram (d) shows the wire moving in the opposite direction to the field, and hence do non cross whatever field lines. Diagram (c) is unlike, indicating a wire moving straight upward perpendicularly to the field and therefore crossing the greatest number of field lines possible at its speed.

The greatest potential difference induced in the wire would occur in diagram (c).

Example five: Agreement Electromagnetic Induction for Circular Motion

Diagram (a) shows a straight slice of copper wire moving along a round path in a uniform magnetic field. Diagram (b) shows the potential difference across the piece of wire against time every bit it does so. If signal in diagram (a) corresponds to point in diagram (b), what bespeak in diagram (a) does point in diagram (b) correspond to?

Answer

Considering these two diagrams, we know that the potential deviation induced in the wire moving in diagram (a) is shown graphically in (b).

Nosotros are also told that bespeak in diagram (a) corresponds to point in diagram (b). This means that when the wire is moving vertically upward, the potential difference induced is positive and takes on its maximum value.

Note that point in diagram (b) occurs where the potential difference is zero. For our wire moving in a magnetic field, the induced potential difference tin can merely be zilch if the wire moves parallel or antiparallel to the surrounding field lines. Therefore, point can but maybe stand for to betoken or signal in diagram (a).

At point , non just is the potential departure across the wire zippo, but nosotros also see from diagram (b) that the potential difference is moving from positive to negative.

Looking back at diagram (a) at signal , the induced potential deviation is moving from negative to positive values (i.e., the wire is transitioning from down to upward motion). At the top of the circle at point , the induced potential difference is moving from positive to negative.

Therefore, of the two points where the wire is moving horizontally, we cull indicate as the one corresponding to point on diagram (b).

Key Points

• When a loop of wire is exposed to a irresolute magnetic field, a potential difference is induced across the wire.
• The faster the magnetic field changes, the greater the corresponding magnitude of the current induced in the wire.
• For a solenoid—a wire coiled in circular loops—the magnitude of induced electric current tin can be increased by adding more loops.
• Current induced in a loop ever points in a direction such that the magnetic field it generates opposes the change in the applied magnetic field that originally induced the electric current, which is a dominion known as Lenz's police force.
• Potential difference will be induced across a straight wire moving in a uniform magnetic field if the wire does not move parallel or antiparallel to the field lines.
• The magnitude of such induced potential difference is proportional to the charge per unit at which the wire crosses magnetic field lines.

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Source: https://www.nagwa.com/en/explainers/383179178013/

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